SCIENCE ABSOLUTE OF SPACE. 53 



(the theorem of Pythagoras for the Euclidean 

 system) ; probably thus also the author de 

 duced it, and the others also follow in the 

 same manner. 



Obviously we have, the powers of e being ex 

 pressed by series (like Tom. I., p. 168), 



1 2.3.4.* 4 



.4 



and so 



=i_2 , 2 , 4 



i 4+ 



- 



3.4.* 4 3.4.5.6.* 6 



= 2+ J~, (designating by 



* 



^ the sum of all the terms after-^ ! ; and we 

 have u=Q, while 2= GO. For all the terms 

 which follow are divided by i 2 ; the first 



k^ k l 



term will be -^; and any ratio &amp;lt;-^; and 



though the ratio everywhere should remain 

 this, the sum would be vTom. I., p. 131), 



3A.i 2 i 2 } &quot;3.4. (* 2 - 



which manifestly =0, while /=oo. 

 And from 



